MATH 115AH Lecture Notes - Lecture 6: Elbit Systems, Linear Map, If And Only If
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Sun . a for v basis necessarilydistinct not. Biz v the inclusion map of sets says a diagram . fine th ) . Quit tdnvn by the coordinate theorem a dnwn is netted defined . i. e a for . S : v w another linear transformation . a. Remarks : up vs say linear transformation from a vstt are completely determined by what they do to a basis, hl says c in the notation and f : b w extend to a linear transformation. V - w : all vstf have basis by axiom. V is a linear combo of finitely many elts from b . so. Let: w be f dust . then dim v = dim w iff. E wi i. wn3 be basis for: w then the map : Vin wi ti extend to a linear transformation . Let: w be fdustt . then dim v - dim w iff.
